A one dimensional character is one who does not have an arc throughout the story. They are the same at the end as they are at the beginning. Many characters in a typical novel or screenplay are one dimensional. They fill small roles and are minor components that reflect the changes the main characters go through. Every “main” character should have more dimension–more of an arc. If your characters are coming off as one dimensional to your readers, that means they are predictable–they repeat the same behavior throughout. Very few people ever do this in reality. Ask me what my wife would do in any given situation and I’ll always have an opinion, but somehow it rarely turns out to be a correct predictor of her behavior; life is just more complex than that. If you have not prepared thorough backstory for a character, they often turn out one dimensional in your mind and therefore comes across that way on the page. I have yet to meet an “evil” person. A “bitch” who believes she is truly a bitch. I have yet to meet a person who is only full of “love”. I meet many people who are well intended, but who become overwhelmed by different aspects of life and then act out in ways that others label.
An older woman in line at the grocery store yells at a young teenager who tried to check out ahead of her–in the 10 items or less line–with a full cart of groceries. The teenager apologizes and says he had not seen the sign. The old woman accuses him of lying and says, “I hope you don’t make it home tonight.”
Only knowing that much, you might consider the old woman a coldhearted, grumpy old bitch. If you are never made privy to other aspects of her life, you are left with a one dimensional impression.
However, if you later find out that the older woman was attacked the previous week by a group of teenage boys who mugged her, knocked her down and took her purse, you might have a differing opinion of her as a person. You might maintain that her attitude in the store was still bitchy, but there is now another dimension that has been added to your understanding of her as a person and where that “bitchy” behavior might have stemmed from.
Repeat this process over and over again and you’ll build multi-dimensional characters that your audience will root for or against and feel emotionally connected to.